I'm working with points in an n-dimensional hyperspherical coordinate system, in other words, my points are in the shape $(r, \theta_1, \theta_2, ..., \theta_{n-1})$. I want to calculate the angle between two points but I'm facing difficulties.
Given two points in an n-dimensional hyperspherical coordinate system, how to compute their cosine similarity?
I know I can first convert them to Cartesian points and then calculate the angle between them, but isn't there a more straightforward way?